Something to think about...

A few days ago, came across a few documentaries that have changed my world for now. It is driving me mad and at the same time leading to some inner peace. The things I always took for granted all my life are being questioned and it is difficult to deal with it! Let me explain…

Well – the first documentary was about "atom".
 
How has humanity's knowledge moved from trying to create gold out of everything to discovery of X-rays to radioactivity to special theory of relativity to general theory of relativity to discovery of neutron to discovery that proton, neutron and electrons are NOT the fundamental particles of atom and then on to big bang and the proof that the big bang really happened.
 
As a secondary thread – and I don't remember the connection now – there was a mention of another scientist whose name I had never heard before – Georg Cantor. He was a mathematician who specialized in "Set Theory"… Yes – the same old boring stuff – natural numbers, rational numbers, series, number of elements in the set, prime numbers, odd numbers, even numbers and …. Infinity!
 
Georg Cantor was obsessed with infinity!
 
He was obsessed with a simple question – how big is infinity?
 
And while coming to the answer of this question – this guy virtually changed the world of mathematics… Look him up on wikipedia… you'll find a lot of detail… They say he lost his sanity because he apparently found the answer to his question which he could never explain to people! The key to his answer was a proof of a concept known as "Continuum Hypothesis". He kept coming up with contradictory proofs that Continuum Hypothesis is TRUE and is FALSE alternately and finally went mad! L
 
He died in 1918 in a sanatorium.
 
The biggest thing about his research that I really find intriguing is – he proved infinity has no single value.
 
In other words, this guy proved that you can have infinite sets that are smaller and larger than each other. i.e., two sets can be infinite but one infinite set can be smaller or larger than the other…
 
This may sound stupid and wrong initially but the proof is disarmingly simple.
 
The set of natural numbers is infinite.
The set of even numbers is infinite too.
The set of natural numbers (because it will include all odd numbers too) will be twice as large!
 
He came up with notations called Aleph to denote different infinite sized sets… I can go on but it gets boring…
 
The biggest thing he came up with was – there is an infinity of infinities! J
 
Like anybody before the time Georg Cantor – Well, I was behind the world – I always took numbers for granted. But because of his work around infinity – I just went through some more articles around set theory and numbers on the internet.
 
Soon I came across another interesting concept – Mathematics and Philosophy.
 
How do these two things relate to each other?
 
Well – they do sound poles apart but they are quite related actually. One obvious connection is infinity itself – what mathematics refers to as infinity is God in philosophy. As philosophy can not define God – so mathematics can not define infinity. In fact, Georg Cantor was a deeply religious man and when he went about his research on infinity he was actually searching for God.
 
Another thing that has caught me even more surprisingly a couple of days ago is a paper about numbers themselves. Just to put it in perspective so that the question is better understood – what are numbers? I mean in terms of existence in real world – what are numbers?
 
For example, if I think about any other fundamental concept – say atom – I have an entity that exists. Or take Abhijeet Kulkarni – he exists. Mama Bathe – exists. The laptop you are looking at now – exists. Number 1 – exists?!? Where is it? Can you show me a number as an existing object? There is a theory that numbers are abstract objects. i.e., they don't exist but they do exist. In people's heads. In terms of making sense of the world, these abstract objects are important.
 
The objection to the abstract object concept comes from those philosophers who oppose trying to make sense of the universe by taking help from things that don't exist in the universe.
 
Their argument is that how can you make sense of an existing, real universe using numbers (read mathematics, theoretical physics and so on) without understanding the basic nature of the entities that you assume exist? You have got no basis to understand the universe using numbers if you don't understand the numbers themselves!!
 
Quite a compelling argument actually…
 
I am lost myself – I don't know what the answer is. I don't know which schools of thought make more sense…
 
I just know one thing – there is a lot to learn still. There is a lot to know still…
 
I just get some deep peace by reading about it all. It is like understanding your own limitations better that lead to an inner peace. Don't know how to put it in words.
 
You guys may think I am on the way of Georg Cantor – read madness J - may be I am!
 
It is just so interesting guys – trying to do something as work and at the same time getting closer to God through your work. The best job in the world can not be any better I think.
 
If we can make a connection between our work and our search for inner peace and God – I think we'll do our work much better. At the same time, we will become better people through the "Bhakti" that we'll achieve through this work!